Summary

Testing the effect of deviance on similarity-based structure and certainty.

Hypothesis: We predict that as a new agent’s deviance from the group stereotype increases there will be a transition from group updating to subgroup formation to subtype formation. This will be reflected in participants’ similarity-rating derived dendrograms. Same as V3

Method changes:

  • only 25%/50%/75% deviancy

  • 600 participants (increased from 300)

  • PNS scale added

Note: data for prediction values are corrected in R script due to coding error

Demographics (Attention Check)
0.25
(N=183)
0.5
(N=184)
0.75
(N=193)
Overall
(N=560)
age
Mean (SD) 35.5 (11.4) 36.8 (13.2) 36.2 (11.3) 36.2 (12.0)
Median [Min, Max] 33.0 [18.0, 79.0] 33.0 [18.0, 93.0] 34.0 [19.0, 75.0] 34.0 [18.0, 93.0]
race
American Indian or Alaska Native 3 (1.6%) 1 (0.5%) 1 (0.5%) 5 (0.9%)
Asian 14 (7.7%) 11 (6.0%) 24 (12.4%) 49 (8.8%)
Black or African-American 9 (4.9%) 13 (7.1%) 13 (6.7%) 35 (6.3%)
Hispanic/Latinx 6 (3.3%) 13 (7.1%) 9 (4.7%) 28 (5.0%)
Other 2 (1.1%) 1 (0.5%) 2 (1.0%) 5 (0.9%)
White 149 (81.4%) 145 (78.8%) 144 (74.6%) 438 (78.2%)
gender
Man 85 (46.4%) 71 (38.6%) 96 (49.7%) 252 (45.0%)
Non-binary 2 (1.1%) 2 (1.1%) 2 (1.0%) 6 (1.1%)
Prefer not to answer 2 (1.1%) 1 (0.5%) 5 (2.6%) 8 (1.4%)
Woman 94 (51.4%) 110 (59.8%) 90 (46.6%) 294 (52.5%)
0.25
(N=15)
0.5
(N=15)
0.75
(N=9)
Overall
(N=39)
age
Mean (SD) 35.3 (14.2) 43.5 (17.6) 37.8 (11.7) 39.0 (15.2)
Median [Min, Max] 28.0 [21.0, 62.0] 39.0 [20.0, 81.0] 34.0 [25.0, 57.0] 34.0 [20.0, 81.0]
race
Asian 3 (20.0%) 1 (6.7%) 0 (0%) 4 (10.3%)
Black or African-American 2 (13.3%) 2 (13.3%) 5 (55.6%) 9 (23.1%)
Hispanic/Latinx 1 (6.7%) 0 (0%) 0 (0%) 1 (2.6%)
White 9 (60.0%) 12 (80.0%) 3 (33.3%) 24 (61.5%)
Other 0 (0%) 0 (0%) 1 (11.1%) 1 (2.6%)
gender
Man 6 (40.0%) 7 (46.7%) 4 (44.4%) 17 (43.6%)
Non-binary 1 (6.7%) 0 (0%) 0 (0%) 1 (2.6%)
Woman 8 (53.3%) 8 (53.3%) 4 (44.4%) 20 (51.3%)
Prefer not to answer 0 (0%) 0 (0%) 1 (11.1%) 1 (2.6%)
Agent Learning Plots
NonDeviant Analysis
Analysis of Deviance Table (Type II Wald chisquare tests)

Response: corrresp
                                   Chisq Df Pr(>Chisq)    
opinion_round                   280.1120  1  < 2.2e-16 ***
Deviant_threshold                10.3110  2   0.005768 ** 
opinion_round:Deviant_threshold   0.2399  2   0.886973    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
 1       opinion_round.trend      SE  df asymp.LCL asymp.UCL z.ratio p.value
 overall              0.0928 0.00555 Inf    0.0819     0.104  16.718  <.0001

Results are averaged over the levels of: Deviant_threshold 
Confidence level used: 0.95 
$emmeans
 Deviant_threshold emmean     SE  df asymp.LCL asymp.UCL z.ratio p.value
 0.25               1.104 0.0516 Inf     1.003     1.205  21.408  <.0001
 0.5                0.992 0.0512 Inf     0.892     1.092  19.387  <.0001
 0.75               0.897 0.0500 Inf     0.799     0.995  17.953  <.0001

Results are given on the logit (not the response) scale. 
Confidence level used: 0.95 

$contrasts
 contrast                                      estimate     SE  df asymp.LCL
 Deviant_threshold0.25 - Deviant_threshold0.5    0.1119 0.0725 Inf   -0.0581
 Deviant_threshold0.25 - Deviant_threshold0.75   0.2067 0.0716 Inf    0.0388
 Deviant_threshold0.5 - Deviant_threshold0.75    0.0948 0.0714 Inf   -0.0725
 asymp.UCL z.ratio p.value
     0.282   1.543  0.2708
     0.375   2.885  0.0109
     0.262   1.329  0.3792

Results are given on the log odds ratio (not the response) scale. 
Confidence level used: 0.95 
Conf-level adjustment: tukey method for comparing a family of 3 estimates 
P value adjustment: tukey method for comparing a family of 3 estimates 
Similarity Plot
Similarity Analysis
Type III Analysis of Variance Table with Satterthwaite's method
                             Sum Sq Mean Sq NumDF DenDF  F value Pr(>F)    
targetpair                      100     100     1   560   0.4284  0.513    
Deviant_threshold             46136   46136     1   560 196.8115 <2e-16 ***
targetpair:Deviant_threshold  26799   26799     1   560 114.3235 <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
$emtrends
 targetpair Deviant_threshold.trend   SE  df lower.CL upper.CL t.ratio p.value
 DN                          -63.27 3.92 560    -71.0   -55.57 -16.141  <.0001
 NN                           -8.44 3.29 560    -14.9    -1.97  -2.561  0.0107

Degrees-of-freedom method: satterthwaite 
Confidence level used: 0.95 

$contrasts
 contrast estimate   SE  df lower.CL upper.CL t.ratio p.value
 DN - NN     -54.8 5.13 560    -64.9    -44.8 -10.692  <.0001

Degrees-of-freedom method: satterthwaite 
Confidence level used: 0.95 
ISM Plot
ISM Analysis
Analysis of Variance Table

Response: k
                   Df  Sum Sq Mean Sq F value   Pr(>F)    
Deviant_threshold   2  34.625 17.3123  33.145 2.51e-14 ***
Residuals         557 290.937  0.5223                     
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
$emmeans
 Deviant_threshold emmean     SE  df lower.CL upper.CL t.ratio p.value
 0.25                1.75 0.0534 557     1.65     1.86  32.823  <.0001
 0.5                 2.12 0.0533 557     2.02     2.23  39.866  <.0001
 0.75                2.36 0.0520 557     2.25     2.46  45.301  <.0001

Confidence level used: 0.95 

$contrasts
 contrast                                      estimate     SE  df lower.CL
 Deviant_threshold0.25 - Deviant_threshold0.5    -0.370 0.0755 557   -0.548
 Deviant_threshold0.25 - Deviant_threshold0.75   -0.603 0.0746 557   -0.778
 Deviant_threshold0.5 - Deviant_threshold0.75    -0.233 0.0745 557   -0.408
 upper.CL t.ratio p.value
  -0.1932  -4.910  <.0001
  -0.4279  -8.088  <.0001
  -0.0576  -3.124  0.0053

Confidence level used: 0.95 
Conf-level adjustment: tukey method for comparing a family of 3 estimates 
P value adjustment: tukey method for comparing a family of 3 estimates 
 Deviant_threshold emmean     SE  df null t.ratio p.value
 0.25                1.75 0.0534 557    2  -4.613  <.0001
 0.5                 2.12 0.0533 557    2   2.328  0.9899
 0.75                2.36 0.0520 557    2   6.856  1.0000

P values are left-tailed 
New Agent Prediction Plot
Prediction Analysis
# A tibble: 2 × 8
  model    term          estimate std.error statistic p.value conf.low conf.high
  <chr>    <chr>            <dbl>     <dbl>     <dbl>   <dbl>    <dbl>     <dbl>
1 below_.5 Deviant_thre…   -17.8       10.9    -1.63    0.103    -39.2      3.61
2 above_.5 Deviant_thre…     6.69      10.9     0.616   0.539    -14.7     28.1 
Analysis of Variance Table

Response: confidence
           Df Sum Sq Mean Sq F value Pr(>F)
deviance    2   1858  929.19  1.3374 0.2634
Residuals 557 386994  694.78               
$emmeans
 deviance emmean   SE  df lower.CL upper.CL t.ratio p.value
 0.25       53.6 1.95 557     49.8     57.4  27.501  <.0001
 0.5        49.1 1.94 557     45.3     52.9  25.283  <.0001
 0.75       50.8 1.90 557     47.1     54.5  26.776  <.0001

Confidence level used: 0.95 

$contrasts
 contrast                    estimate   SE  df lower.CL upper.CL t.ratio
 deviance0.25 - deviance0.5      4.45 2.75 557    -2.01    10.92   1.619
 deviance0.25 - deviance0.75     2.78 2.72 557    -3.61     9.17   1.023
 deviance0.5 - deviance0.75     -1.67 2.72 557    -8.05     4.71  -0.616
 p.value
  0.2386
  0.5628
  0.8115

Confidence level used: 0.95 
Conf-level adjustment: tukey method for comparing a family of 3 estimates 
P value adjustment: tukey method for comparing a family of 3 estimates 
Moderator: Last Opinion
0.25
(N=183)
0.5
(N=184)
0.75
(N=193)
Overall
(N=560)
pred_maj
Yes 151 (82.5%) 143 (77.7%) 153 (79.3%) 447 (79.8%)
No 32 (17.5%) 36 (19.6%) 36 (18.7%) 104 (18.6%)
Missing 0 (0%) 5 (2.7%) 4 (2.1%) 9 (1.6%)
# A tibble: 4 × 9
# Groups:   pred_maj [2]
  pred_maj id      term  estimate std.error statistic p.value conf.low conf.high
  <lgl>    <chr>   <chr>    <dbl>     <dbl>     <dbl>   <dbl>    <dbl>     <dbl>
1 FALSE    below_… Devi…    -5.56      22.6    -0.246   0.807    -50.7     39.6 
2 FALSE    above_… Devi…    27.1       21.2     1.28    0.206    -15.3     69.5 
3 TRUE     below_… Devi…   -17.6       12.1    -1.45    0.147    -41.4      6.22
4 TRUE     above_… Devi…     1.45      12.5     0.116   0.908    -23.1     26.0 
Analysis of Variance Table

Response: confidence
                   Df Sum Sq Mean Sq F value    Pr(>F)    
deviance            2   1651   825.4  1.2296    0.2932    
pred_maj            1  13775 13774.9 20.5192 7.258e-06 ***
deviance:pred_maj   2   1303   651.3  0.9701    0.3797    
Residuals         545 365868   671.3                      
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
0.25
(N=183)
0.5
(N=184)
0.75
(N=193)
Overall
(N=560)
pns_med
High 76 (41.5%) 86 (46.7%) 106 (54.9%) 268 (47.9%)
Low 107 (58.5%) 98 (53.3%) 87 (45.1%) 292 (52.1%)
# A tibble: 4 × 9
# Groups:   pns_med [2]
  pns_med id       term  estimate std.error statistic p.value conf.low conf.high
  <chr>   <chr>    <chr>    <dbl>     <dbl>     <dbl>   <dbl>    <dbl>     <dbl>
1 High    below_.5 Devi…   -17.7       16.4    -1.08    0.282    -50.1      14.7
2 High    above_.5 Devi…    15.1       15.0     1.00    0.317    -14.6      44.7
3 Low     below_.5 Devi…   -18.9       14.7    -1.29    0.199    -47.8      10.0
4 Low     above_.5 Devi…    -5.57      15.7    -0.354   0.724    -36.6      25.4
Analysis of Variance Table

Response: confidence
                  Df Sum Sq Mean Sq F value  Pr(>F)  
deviance           2   1858  929.19  1.3430 0.26190  
pns_med            1   2823 2823.03  4.0804 0.04387 *
deviance:pns_med   2    882  440.84  0.6372 0.52916  
Residuals        554 383289  691.86                  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Order of deviant across rounds
Opinion Round
0
(N=560)
1
(N=560)
2
(N=560)
3
(N=560)
4
(N=560)
5
(N=560)
6
(N=560)
7
(N=560)
8
(N=560)
9
(N=560)
10
(N=560)
11
(N=560)
Overall
(N=6720)
trialnum
0 98 (17.5%) 91 (16.3%) 86 (15.4%) 96 (17.1%) 92 (16.4%) 89 (15.9%) 91 (16.3%) 97 (17.3%) 98 (17.5%) 101 (18.0%) 99 (17.7%) 83 (14.8%) 1121 (16.7%)
1 107 (19.1%) 82 (14.6%) 97 (17.3%) 95 (17.0%) 87 (15.5%) 99 (17.7%) 105 (18.8%) 90 (16.1%) 98 (17.5%) 90 (16.1%) 102 (18.2%) 98 (17.5%) 1150 (17.1%)
2 99 (17.7%) 93 (16.6%) 98 (17.5%) 88 (15.7%) 88 (15.7%) 110 (19.6%) 86 (15.4%) 97 (17.3%) 102 (18.2%) 79 (14.1%) 100 (17.9%) 113 (20.2%) 1153 (17.2%)
3 89 (15.9%) 92 (16.4%) 114 (20.4%) 93 (16.6%) 95 (17.0%) 90 (16.1%) 94 (16.8%) 93 (16.6%) 86 (15.4%) 100 (17.9%) 83 (14.8%) 90 (16.1%) 1119 (16.7%)
4 84 (15.0%) 113 (20.2%) 88 (15.7%) 98 (17.5%) 96 (17.1%) 80 (14.3%) 95 (17.0%) 82 (14.6%) 91 (16.3%) 87 (15.5%) 78 (13.9%) 78 (13.9%) 1070 (15.9%)
5 83 (14.8%) 89 (15.9%) 77 (13.8%) 90 (16.1%) 102 (18.2%) 92 (16.4%) 89 (15.9%) 101 (18.0%) 85 (15.2%) 103 (18.4%) 98 (17.5%) 98 (17.5%) 1107 (16.5%)
Things to note
  • The PNS moderator is a median split
Unresolved
  • U shaped analysis, issue for all studies